cultural goods production, cultural capital formation and the provision of cultural services
TRANSCRIPT
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Cultural Goods Production, Cultural Capital Formation and the Provision
of Cultural Services∗
By
Sao-Wen Cheng
FB5, VWL IV, University of Siegen
Hoelderlinstr. 3, 57068 Siegen, Germany
Tel.: +49 - 271 - 740 4534
Fax: +49 - 271 - 740 2732
Email: [email protected]
Abstract
Cultural capital is assumed to benefit all members of society. It is accumulated through the
consumption of cultural services and is diminished through depreciation. Using the stock of
cultural goods, cultural services are provided by the cultural services industry; the stock of
cultural goods is enlarged by the flow of new cultural goods created by individuals who are
both consumers and creators of culture and whose utility is positively affected by the cultural
goods they created. In the no-policy market economy, individuals tend to ignore the positive
external effects of their cultural services consumption and creation of cultural goods on other
individuals via augmenting cultural capital and cultural-goods stock. Consequently, less cul-
tural capital and cultural-goods stock will be accumulated. The efficient allocation can be
restored by introducing an appropriate subsidy that stimulates the consumers’ demand for
cultural services, and the creation of new cultural goods, promotes the accumulation of cul-
tural capital and cultural goods.
Jel-code: H2, H3, Z1
Keywords: cultural capital, cultural services, cultural goods
Version: 17. Jan. 2005
∗ This paper is part of my dissertation.
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1 Introduction
Unintendedly, social beneficial effects emerge from individuals’ participation in cultural ac-
tivities (e.g. when attending concerts to derive private pleasure): crime will be reduced, liv-
ing-together in community will be more harmonious and creativity and innovative ability will
be further developed.1 Though economists have extensively discussed the concept of positive
externality, they either claim an underprovision of culture without further specifying what the
concrete link between culture and externality is like, (cf. e.g. Robbins (1963, p. 58) and Bau-
mol and Bowen (1966, p. 382n.)), or they list various externalities and invoke them to justify
public support for culture, (cf. e.g. Netzer (1978, p. 22n) and Fullerton (1992, p. 80)). While
all these positive externality arguments have some appeal in the cultural context, they are not
made precise in formal intertemporal analysis and they do not explicitly account for the dis-
tinctive characteristics of culture. Though Ulibarri (2000) provides a dynamic framework to
develop a theory of rational philanthropy in forming “cultural capital”, he rather focuses on
the interdependence between capital market opportunities and public funding for culture.
This paper first specifies culture in three aspects as cultural goods, cultural services and cul-
tural capital in a dynamic stock-flow model; it then distinguishes and focuses on the relations
between these different aspects of culture. Next it models the social components of the con-
sumption of culture via a process of accumulation (and depreciation) of cultural capital (fol-
lowing Pethig and Cheng (2002)), the creation of new cultural goods to build up the stock of
cultural goods, which in turn has an effect on the individuals’ well-being. While the present
paper doesn’t aim at surveying and comparing various notions of culture and related terms
applied in the literature, it is necessary to define the terms, cultural goods, cultural services
and cultural capital specifically for the purpose of the subsequent analysis.
Cultural goods2 are considered to consist of tangible or intangible items of cultural signifi-
cance like heritage buildings, sites, locations, works of arts (e.g. paintings, sculptures), litera-
ture and music etc. There is a stock of cultural goods inherited from the past, and there is an
ongoing process of creating new cultural goods which are then added to the stock. Following
Throsby (1999, p. 7) we assume the cultural heritage to “…give rise to a flow of services that
1 For empirical investigations see e.g. UNESCO (1998), Part one. 2 The notion of cultural goods as introduced here is closely related to what is termed “cultural capital” by
Throsby (1999), except that we do not link cultural goods with Thorsby’s “cultural value”. The latter is considered by Throsby (1999, p.6) as “…different from, though not unrelated to economic value”, but Throsby does not specify how this value emerges. UNESCO (2000) describes cultural goods as follows: “Cultural goods…are the result of individual or collective creativity, include printed matter and literature,
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may be consumed as private and/or public goods entering final consumption immediately,
and/or they may contribute to the production of future goods and services, including new cul-
tural goods”. Suppressing the role of these services as productive factors we focus on con-
sumptive cultural services, called cultural services 3. Cultural services are considered to be all
cultural performances provided by cultural institutions. These cultural services may take
many widely differing forms such as visits to museums, attendances of concerts or reading
books. Implicitly, the meaning and importance of cultural heritage for society is closely
linked to the number and kinds of cultural services flowing from the stock of cultural goods.
The magnitude and the structure of those flows depend, in turn, to a large extent on costs of
providing them and on income and relative prices to consume them. Public cultural policies,
intervention and regulation may have a great impact on these economic determinants. Conse-
quently, the stock of cultural goods can facilitate the provision of cultural services, but there
is no automatism in the cultural heritage “giving rise to a flow of cultural services”.
Our principal hypotheses are that the continuous consumption of cultural services over time
leads to an accumulation of cultural capital4, and the continuous creation of new cultural
goods leads to an increase of the stock of cultural goods. Both stocks are positively valued by
all members of society.
Following Becker (1998, p. 12n.) we conceive of cultural capital as an intangible and depre-
ciable asset that is a form of social capital in the sense of Coleman (1990) who argues
(ibidem, p. 317) that “...social capital [and hence cultural capital, as presently defined; the
author] is an important resource for individuals and can greatly affect their ability to act and
their perceived quality of life.”
Introducing cultural goods and cultural capital as outlined above in dynamic setups implies
that the greater is the stock of cultural goods, the greater is the probability that the flow of
cultural services is broad, even though the link between both is not rigid; the more cultural
services are consumed the more cultural capital is likely to be generated, after depreciation is
accounted for, and the greater will be the external benefits provided for society. Though con-
sumers may account for their own benefits derived from increases in the stock of cultural
music, visual arts, cinema and photography, radio and television, games and sporting goods”. In spirit this description is quite close to the term we use here.
3 Some other authors combine the terms “cultural services” and “cultural goods” used here as “cultural goods”. E.g. Towse (2003, p. 2) argues that “cultural goods are tangible objects, such as an artwork or a book; others are intangible services, like a musical performance or a visit to museum”. Such a view total-ly ignores the productive effects of cultural goods on cultural services and therefore doesn’t provide a solid basis for rigorous analysis, in our opinion.
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goods/cultural capital brought about by their own creation of cultural goods and consumption
of cultural services, they tend to ignore the beneficial impact which their own contribution to
the generation of cultural goods or cultural capital has on their fellow citizens. This myopic
individual behavior gives rise to external cultural benefits.
The basic idea to be developed in the present paper is hence the insight, aptly expressed by
Heller and Starrett (1976, p. 10) that “one can think of externalities as nearly synonymous
with non-existence of markets”. In their view an externality “is a situation in which the pri-
vate economy lacks sufficient incentives to create a potential market in some good and the
nonexistence of this market results in losses in Pareto efficiency”. This paper aims at estab-
lishing a benchmark economy, in which an optimal intertemporal allocation is characterized
by introducing Lindahl prices (1919) to eliminate the market failure. This set-up turns out to
imply that under the condition that all agents reveal their willingness-to-pay for public goods
truthfully, the market mechanism indeed implements the optimal intertemporal allocation.
Lindahl markets are highly artificial since they are based on the problematic assumption that
the agents truthfully reveal their willingness-to-pay for public goods. Yet agents have an in-
centive to underreport their willingness-to-pay and this is why Lindahl markets don’t emerge
in real market economies. The corresponding markets economies are shown to be allocative
inefficient. The main conclusion in the present paper is that the market failure can be cor-
rected by introducing an appropriate Pigouian tax/subsidy scheme, in which the cultural ex-
ternalities can be internalized, such that consumer’s demand for cultural services and her
creation of new cultural goods will be stimulated, the accumulation of cultural capital and
cultural-goods stock will be promoted.
The paper is organized as follows. In section 2 the general theoretical basis is modeled. Sec-
tion 3 characterizes an efficient intertemporal allocation, which is decentralized in section 4
by Lindahl prices. Section 5 proceeds on the assumption that Lindahl markets do not exist and
derives cultural policy recommendation to restore the allocation distortion caused by missing
markets. Section 6 concludes.
2 The general model
Consider an economy in which a single composite resource serves as an input to produce
three goods: a private consumer good, new cultural goods and cultural services. Society con-
4 The stock of cultural goods as defined in the present study is denoted “cultural capital” by some other
authors, e.g. Bourdieu (1983) and Throsby (1999). As will be clarified below we use the terms “cultural capital” here in an entirely different way.
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sists of cn individuals who are not only consumers but also creators of new cultural goods
and hence are producers in that capacity. Therefore we will model individuals as consumer-
artists5. The representative consumer-artist’s utility function is
( ), , , , .
c c c c cu U g k s v y=+ + + + +
(1)
and c cg k represent the consumer-artist’s demand for the stock of cultural goods and cultural
capital which will be specified and interpreted further below. cs is her consumption of cultur-
al services, cv is the amount of new cultural goods created by her, and cy is her consumption
of the consumer good.
As an artist, she possesses cultural and technical skills to produce new cultural goods using
the production function
( ) ,c v cv V r ,k=+ +
(2)
where vr is the resource input to produce the amount cv of new cultural goods, given the in-
put ck of cultural capital. The stock of cultural capital, ck , as an argument of the production
function (2) expresses the hypothesis that a diffusing creativity-stimulating atmosphere in
society induces the artists to create more artworks.
New cultural goods, cv , constitute investments in the stock of cultural goods, g. This stock
changes over time according to the investment function
c c gg n v gα= −& . (3)
The state variable, g, is the stock of cultural goods created by all artists and known to exist at
time t. We refer to g as the stock of cultural goods supplied at time t. It is inherited from the
past (cultural heritage), and there is an ongoing process of degradation at an exogenous posi-
tive rate of depreciation gα , reflecting the observation that some fraction of cultural goods
gets lost over time either physically or in the memory of the artists and society at large. Ex-
amples are the destruction of the historical statues of the Bamiyan Buddhas in Afghanistan
under the Taliban regime. As shown in (3), the depreciation of the stock of cultural goods,
g gα , is countervailed by adding the newly created cultural goods to it, c cn v , such that the net
increment of the stock of cultural goods may be positive or negative.
5 The notion of “artist” is used here as a synonym for “creator of new cultural goods”.
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As expressed in (1), consumers are affected by the stock of cultural goods (or by parts of it) in
two different ways:
(i) The mere existence of cultural goods may give satisfaction to people, it may make them
happy and/or proud. This existence value or passive-use value of cultural goods is captured in
(1) through cgU 0> .
(ii) Individuals make use of cultural goods actively through consuming cultural services: The
Mona Lisa painting is enjoyed by visiting the Louvre in Paris or by looking at one of its pho-
tos, prints or replicas; Beethoven’s 9th is consumed by attending a live concert or by listening
to a radio broadcast or the CD-player. The benefit derived from consuming cultural services is
captured in (1) through csU 0> .
To further illustrate the important distinction between passive use (g) and active use (s) con-
sider the Chinese terracotta army hidden underground for some 2500 years. Before it was
(re)discovered in the 1970s it did not belong to the stock of (known) cultural goods, g. It was
then added to that stock through reports in the media. But beyond basic information about its
existence people were eager to learn more about it, and this demand was satisfied through
restoration and the supply of various cultural services ranging from art books, replicas and
access to the site.
In our model, cultural services are produced by sn identical firms with the help of the produc-
tion functions
( ), ,
s s ss S r g=+ +
(4)
where ss are cultural services produced by the cultural-services firm with resource input sr
and cultural-goods input sg . An art gallery exhibiting Leonardo da Vinci’s Mona Lisa needs
to possess that painting as an input. If Beethoven’s 9th symphony is performed in a concert
hall, the musicians need to have the scores of that symphony etc.
The specification of the production functions (2) and (4) appears to be quite plausible al-
though it may be argued, for example, that in addition to the inputs vr and ck in (2), sg may
also be a factor stimulating the individuals’ creativity in generating new cultural goods,
cgV 0> , and likewise, kS 0> . Yet in what follows we will stick to the production functions
(2) and (4) to avoid unreasonable analytical complexity.
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Cultural capital is conceived of as an intangible and depreciable asset that is built up by con-
suming cultural services. Similar to (3) the formation of cultural capital, k, is modeled as a
dynamic process:
c c kk n s kα= −& , (5)
where kα is an exogenous positive rate of depreciation accounting for the observation that
some fraction of the stock of cultural capital gets lost over time. For example, the Chinese
Cultural Revolution during the 1960s greatly diminished the Chinese society’s cultural capital
implying that, on the one hand, the external benefits provided by cultural capital declined and
that, on the other hand, the Chinese culture became less and less valued by the Chinese socie-
ty.
The distinction between, and separate consideration of, the stock of cultural goods and the
stock of cultural capital in the model and as arguments in the consumer’s utility function is
motivated by the observation that the existence of cultural goods per se is not an appropriate
indicator of a society’s intensity of cultural life and its cultural atmosphere. The stock of cul-
tural goods needs to be “activated” to create a cultural atmosphere or - as we call it - cultural
capital. That is achieved through the supply and consumption of cultural services which, in
turn, are based on cultural goods as an essential input. Therefore the stock of cultural goods
has an impact on the accumulation of cultural capital, (5), only indirectly through (4). In other
words, the (aggregate) amount of cultural services consumed is related to but is not unambi-
guously determined by the size of the (aggregate) stock of cultural goods: Societies with a
rather small cultural heritage (low g) may be culturally very active (high s) and vice versa.
Hence it is not the stock of cultural goods per se that determines the cultural atmosphere or
cultural climate in society but primarily the volume and richness of cultural services through
which the existing stock of cultural goods is used by the members of society. Our principal
hypothesis is that the continuous consumption of cultural services leads to an accumulation of
cultural capital which, in turn, is positively valued by all members of society.
It remains to introduce the production of a private consumer good that is produced by a single
(aggregate) firm using the technology
( ) ,
yy Y r=+
(6)
where y is the amount of the consumer goods produced by the resource input yr .
The description of our model will now be completed by listing all supply constraints:
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c cy n y> , (7)
c c y s s c vn r r n r n r≥ + + , (8)
ck k≥ , (9)
cg g≥ , (10)
sg g≥ , (11)
s s cn s s≥ . (12)
The constraints (9) - (12) characterized cultural capital, the stock of cultural-goods and cul-
tural services, respectively, as public goods. The structure of the model is summed up in a
non-technical way in Table 1.
Table 1: General structure of the model
Cultural capital k New cultural Stock of Cultural Consumer goods cultural goods services goods v g s y
( ),vV r k+ + ( ),s sS r g
+ + ( )yY r
+
Constant resource endowment r
Table 1 shows that the economy’s given resource endowment is used to produce three differ-
ent types of goods: an ordinary (private) consumer goods, y, new cultural goods, v, and cul-
tural services, s. While consumer goods are produced with resources as the only input, extant
cultural goods are an essential additional input in the process of producing cultural services.
Regarding the creation of new cultural goods it is assumed that cultural capital has a produc-
( )Consumption , , , ,U k g s v y+ + + + +
9
tivity enhancing effect. All three kinds of goods produced are demanded by consumers. In
addition, consumers derive satisfaction from both cultural capital and the prevailing stock of
cultural goods. These two stocks are not “produced” in a technical sense but they accumulate
(or deplete) over time according to some specific stock-flow relationships modeled in (3) and
(5), respectively. The driving force for the accumulation of cultural goods is the creation of
new cultural goods by all consumer-artists, while the accumulation of cultural capital is de-
rived by the aggregate consumption of cultural services.
3 Allocative efficiency
The social planner aims at maximizing the Utilitarian welfare function
( ), , , ,tc c c c c c
0
n e U g k s v y dtδ∞
−∫ , subject to (2) - (12), (13)
where δ is a positive and constant social discount rate. Hence the planner has to solve a prob-
lem of optimal control where the time path of the state variables g and k is guided by the con-
trol variables , , , , , , , , , and c s c c s c s v y cg g k s s v r r r y y . To characterize the socially optimal in-
tertemporal allocation, consider the following Hamiltonian associated to the social planner’s
optimization problem:
( ) ( ) ( ) ( )c c c c c c g c c g k c c k y yH n U g ,k ,s ,v , y n v g n s k Y r yμ α μ α λ ⎡ ⎤= + − + − + −⎣ ⎦
( ) ( ) ( ), ,s s s s s c v v c c r c c y s s c vn S r g s n V r k v n r r n r n rλ λ λ⎡ ⎤ ⎡ ⎤+ − + − + − − −⎣ ⎦ ⎣ ⎦
( ) ( ) ( ) ( ) ( )c c c c sc s s c c gc c s gs s c k cy n y n n s s n g g n g g n k kλ λ λ λ λ+ − + − + − + − + − , (14)
where and g kμ μ are co-state variables and λ’s denote Lagrangean multipliers. The asso-
ciated marginal conditions are enumerated in the first column of Table 2. The characteristics
of the optimal time path for cultural goods are spelled out after some rearrangement of these
pertinent marginal conditions as follows:
g v
y r r y r
U1U Y V U Yμ
= − , (15)
Table 2: Comparison of rules governing a socially optimal allocation and an equilibrium in the market economy
GM BM BL
1 2 3 1
( )/ck k r k rU V Vλ λ= − ( )/
ck c kc c r k rU p p V Vβ β= − -
2
cg gcU λ= cg c gcU pβ= /g c g cU nβ τ=
3
v r r g rU V Vλ μ= − v r c r c v rU V p p Vβ β= − v r c r c v rU V p p Vβ β= −
4
s sc kU λ μ= − s c sc c sKU p pβ β= − s c sc c scU pβ β τ= +
5
r c sc rn Sλ λ= r s rp p S= r s rp p S=
6
gs c sc gn Sλ λ= gs s gp p S= gs s gp p S=
7 ( )g g g c gc s gsn nμ δ α μ λ λ= + − −& ( )g g v gp pϕ δ α= + −& ( )g g v g gp pϕ δ α τ= + − −&
8 ( )k k k c knμ δ α μ λ= + −& ( )k k sK kp pϕ δ α= + −& -
9
r y rYλ λ= r y rp p Y= r y rp p Y=
10
11
( ) ( ) ( )
g gc s
g y r vr
r y rg r r g g
U Sn nU Y US 1V U YU Y
μ
δ α δ α δ α
⎧ ⎫⎡ ⎤⎪ ⎪⎢ ⎥ ⎛ ⎞⎪ ⎪⎢ ⎥= − + − −⎜ ⎟⎨ ⎬⎜ ⎟⎢ ⎥+ + +⎪ ⎪⎝ ⎠⎢ ⎥⎪ ⎪⎢ ⎥⎣ ⎦⎩ ⎭
&. (16)
[1] = -{( [2] + [3] ) - ( [4] - [5] )}.
g y r/ U Yμ is the shadow price of cultural goods produced by consumer-artists in terms of the
resource. According to (15) the shadow price of cultural goods equals the difference between
the individual’s marginal cost of producing new cultural goods (i.e. her marginal investment
cost) and her marginal benefit from creating new cultural goods. Ceteris paribus, the shadow
price goes up when the investment is successively increased and vice versa. In (16), [1] is the
present value of the change in time of the shadow price of cultural goods (in terms of the re-
source). [2] is the present value of the consumers’ aggregate marginal passive-use benefits
from cultural goods. [3] is the present value of the aggregate marginal productivity effect of
cultural goods in the production of cultural services. ([4] - [5]) is the marginal social cost of
cultural goods while ([2] + [3]) is their marginal social benefit. Closer inspection of (16)
yields
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ] [ ]( ) [ ]g 0 2 + 3 4 - 5 2 + 3 5 4μ> < <⎧ ⎫ ⎧ ⎫ ⎧ ⎫⎪ ⎪ ⎪ ⎪ ⎪ ⎪= ⇔ = ⇔ + =⎨ ⎬ ⎨ ⎬ ⎨ ⎬< > >⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩ ⎭ ⎩ ⎭ ⎩ ⎭
& ,
which indicates that if the marginal social benefit of cultural goods is smaller than (equal to,
greater than) the marginal social cost of cultural goods, the shadow price of cultural goods
declines (keeps unchanged, increases) over time.
After having investigated the optimal time path for cultural goods, we now turn to the charac-
teristics of the optimal path for cultural capital that are elicited from the marginal conditions
as
k sc
y r c r y r
U1 1 nU Y n S U Yμ ⎛ ⎞
= −⎜ ⎟⎜ ⎟⎝ ⎠
, (17)
( ) ( ) ( )
k kc c
y rk src
k y r k k c r y r
U Vn nU Y UV 1 1 nU Y n S U Y
μδ α δ α δ α
⎧ ⎫⎡ ⎤⎪ ⎪⎢ ⎥ ⎛ ⎞⎪ ⎪⎢ ⎥= − + − −⎜ ⎟⎨ ⎬⎜ ⎟⎢ ⎥+ + +⎪ ⎪⎝ ⎠⎢ ⎥⎪ ⎪⎣ ⎦⎩ ⎭
&. (18)
[6] = -{( [7] + [8] ) - c
1n
( [9] - [10] )}.
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The shadow price of cultural capital (in terms of the resource) has a similar structure as that of
cultural goods. It is the 1 / ncb gth part of the difference between the marginal resource cost of
production and the consumers’ aggregate marginal willingness-to-pay for cultural services.
From the viewpoint of cultural-capital formation, the marginal benefits of cultural services
accruing to consumers ( sU > 0) constitute a positive externality. Hence the aggregate mar-
ginal willingness-to-pay for cultural services reduces the marginal social costs of cultural cap-
ital. In (18), [6] is the present value of the change in time of the shadow price of cultural capi-
tal. [7] is the present value of the consumers’ aggregate marginal benefits from cultural capi-
tal. [8] is the present value of the aggregate marginal productivity effect of cultural capital in
the production of new cultural goods. ([9] - [10]) is the 1 / ncb gth part of the marginal social
cost of cultural capital while ([7] + [8]) is their marginal social benefit. (18) implies
[ ] [ ]( ) [ ] [ ]( ) [ ] [ ] [ ] [ ]kc c c
1 1 10 7 + 8 9 - 10 7 + 8 10 9n n n
μ> < <⎧ ⎫ ⎧ ⎫ ⎧ ⎫⎛ ⎞⎪ ⎪ ⎪ ⎪ ⎪ ⎪= ⇔ = ⇔ + =⎨ ⎬ ⎨ ⎬ ⎨ ⎬⎜ ⎟< > >⎝ ⎠⎪ ⎪ ⎪ ⎪ ⎪ ⎪⎩ ⎭ ⎩ ⎭ ⎩ ⎭
& ,
which says that if the marginal social benefit of cultural capital is smaller than (equal to,
greater than) the marginal social cost of cultural capital, the shadow price of cultural capital
declines (keeps unchanged, increases) over time.
A steady state of the socially optimal time path is defined by & , &k k= =0 0μ and gg 0, 0μ= =& & .
In view of (3), (5), (16) and (18) it is straightforward to characterize such a steady state by
c c gn v gα= , (19)
c c kn s kα= , (20)
[2]+[3]+[5]=[4] or ( ) ( )
g gc s
y r vr
y r rg g
U Sn nU Y US 1U Y Vδ α δ α
+ + =+ +
, (21)
[7]+[8]+c
1n
[10] =c
1n
[9] or ( ) ( )
k kc c
y r sr
k k y r c r
U Vn nU Y UV 1U Y n Sδ α δ α
+ + =+ +
. (22)
According to (19) and (20), new cultural goods constituting the investments in the stock of
cultural goods must equal the depreciation of that stock, and the accumulated cultural capital
through the consumption of cultural services must equal the loss of cultural capital through
depreciation in the steady state. The interpretation of (21) and (22) is obvious: The marginal
production costs of new cultural goods and cultural services, respectively, on the right side of
13
these equations are exactly matched by the respective marginal benefits of these goods. (21)
and (22) are the modified version of the famous summation condition of Samuelson (1954, p.
387-389) for the optimal allocation of public goods.
4 The Lindahl economy as a benchmark
Now we explore how the market mechanism performs in the context of cultural economics as
modeled here and, in particular, under which conditions it is possible to implement the optim-
al allocation through the market mechanism. To answer these questions, we make use of stan-
dard welfare economic methodology to study how the optimal intertemporal allocation can be
“decentralized by prices. The personalized prices a la Lindahl (1919) derived here serve as a
benchmark (denoted as BM) for later reference. The market economy we envisage in the
present section exhibits a complete set of perfectly competitive markets, some of which will
turn out to be purely virtual or fictitious. The market economy is made up of five different
types of agents. All of them are price takers and we characterize them by their market transac-
tions and the optimization problems they solve.
● The representative consumer-artist carries out the following transactions:
- She sells her resource endowment cr at price rp and buys back her own demand for the
resource, vr , at the same price, to create new cultural goods.
- She sells her newly created cultural goods, cv , to firm G (to be specified below) at price
vp .
- She buys the amount cg of cultural goods from firm G at price gcp .
- She buys the amount cs of cultural services for own consumption at price scp , and sells
the amount cKs of cultural services consumed to the firm K at price sKp .
- She buys the amount ck of cultural capital from firm K at the price kcp ; like cg (see
above) ck is treated here as the consumer-artist’s endogenous decision variable.
- She buys private consumer goods, cy , at price yp .
All these transactions listed above are subject to the budget constraint
sK cK v c r c c gc c kc c r v sc c y cp s p v p r p g p k p r p s p yπ+ + + ≥ + + + + , (23)
14
where cπ is consumer-artist’s share of profits, taken as constant by her. The consumer-artist
aims at maximizing the present value of her utility
( )( )
c c c c cK c c
tc c c c cg , k , r , s , s , v , y
0
Max U g ,k ,s ,v , y e dtδ∞
−∫ ,
subject to ( )c v c cK cv V r ,k , s s= ≤ and (23). (24)
The pertinent Hamiltonian reads
( ) ( ) ( )Cc c c c c vc v c c S c cKH U g ,k ,s ,v , y V r ,k v s sβ β⎡ ⎤= + − + −⎣ ⎦
c sK cK v c r c c gc c kc c r v sc c y cp s p v p r p g p k p r p s p yβ π⎡ ⎤+ + + + − − − − −⎣ ⎦ . (25)
● Firm Y buys the resource, yr , at price rp , produces the consumer goods y, and sells them
to the consumer-artists at price yp . Firm Y hence maximizes the present value of its profit:
( )( )
y
ty r y
y , r 0
Max p y p r e dtδ∞
−−∫ , subject to (6). (26)
Firm Y’s optimization calculus is to solve the Hamiltonian:
( )Yy r y y yH p y p r Y r yβ ⎡ ⎤= − + −⎣ ⎦ . (27)
● The representative cultural-cervices firm produces cultural services, ss . It buys the re-
source input, sr , at price rp , and cultural-goods input (taken from the stock of cultural
goods), sg , at the price gsp . The demand price of cultural services, as introduced above, is
scp . Hence the cultural-services producer’s revenue from selling one and the same unit of its
output to all demanders is c scn p . In what follows it is analytically convenient to assume that
the cultural-services firm’s supply of cultural services, ss , is (intended to be) sold to all cn
consumer-artists at some (aggregate) supply price sp . As will be shown further below, a ne-
cessary equilibrium condition will then turn out to be s c scp n p= . The cultural-services firm
maximizes the present value of its profit:
( )( )
s s s
ts s r s gs sg , r , s 0
Max p s p r p g e dtδ∞
−− −∫ , subject to (4). (28)
The pertaining optimal production is attained by solving the Hamiltonian:
( )Ss s r s gs s sj s s sH p s p r p g S g ,r sβ ⎡ ⎤= − − + −⎣ ⎦ . (29)
15
● Firm G purchases new cultural goods, Gv , at price vp from the consumer-artists and sells
cultural goods, Gg , from the stock of cultural goods, g, to all cultural-service firms and to all
consumer-artists, where Gg is now firm G’s decision variable and g is the state variable. (In
equilibrium the condition Gg = g needs to be satisfied). Recall that gsp is the price the cultur-
al-services firm pays for each unit of cultural goods purchased. Hence firm G accrues the rev-
enue s gsn p per unit of cultural goods sold to all cultural-service firms. Likewise, the consum-
er-artist buys a unit of cultural goods from firm G at price, gcp . It follows then that firm G
obtains the revenue c gcn p per unit of cultural goods sold to all consumer-artists. Hence if firm
G sells a unit of cultural goods to each and every cultural-services firm and to each and every
consumer-artist, its total revenue is ( )s gs c gc Gn p n p g+ . Obviously the argument is essentially
like that applied above for the market of cultural services. It suffices, therefore, to introduce
an aggregate supply price, gp , for firm G (which will need to satisfy g s gs c gcp n p n p= + in
equilibrium). With this set-up, firm G maximizes the present value of its profit:
( )G G
tg G v Gg ,v 0
Max p g p v e dtδ∞
−⎡ ⎤−⎣ ⎦∫ , subject to andG g Gg v g g gα= − ≤& . (30)
The associated Hamiltonian reads:
( ) ( )Gg G v G g G g G GH p g p v v g g gϕ α β= − + − + − , (31)
where gϕ is the co-state variable associated to the state variable g.
● Firm K is a fictitious agent, who buys cultural services consumed by the consumer-artists,
Ks , at price sKp and sells the cultural capital, Kk from the stock of cultural capital, k, at the
aggregate supply price kp . The supply price needs to satisfy the condition k c kcp n p= in
equilibrium. Firm K maximizes the present value of its profits,
( )
[ ]K K
tk K sK Kk , s 0
Max p k p s e dtδ∞
−−∫ , subject to andK k Kk s k k kα= − ≤& . (32)
Technically speaking, Kk belongs to firm K’s control variables whereas k is cultural capital
as a state variable. Note also that the condition Kk k= needs to be satisfied in equilibrium.
Firm K sells Kk to the consumer-artists. In view of (32), firm K can be interpreted as a public
16
enterprise maximizing the present value of the intangible asset “cultural capital” Kk . The
pertinent Hamiltonian is
[ ] ( ) ( )Kk K sK K k K k K KH p k p s s k k kϕ α β= − + − + − , (33)
where kϕ is the co-state variable associated to the state variable k.
The marginal conditions derived from solving (25), (27), (29), (31) and (33) are listed in the
second column of Table 2. We now investigate how this hybrid market equilibrium fares in
terms of allocative efficiency6 by following the standard procedure of comparing the marginal
conditions of the efficient regime in section 3 with the marginal conditions derived above.
The result is summarized in
Proposition 1
Set y yp 1λ= ≡ , ggc
y
Up
U= , gs gsp λ= , k r k
kcy r
U VpU V
λ= + , s sp λ= , sc scp λ= , sK kp μ= ,
v gp μ= , r rp λ= , g gsg c s
y y
Up n n
Uλλ
= + and k v kk c
y y
U Vp nU
λλ
⎛ ⎞= +⎜ ⎟⎜ ⎟
⎝ ⎠, where all terms on the
right side of the equations are evaluated at the solution of maximizing (13) subject to (2) -
(12). Then at each point in time a general competitive equilibrium is attained in economy BM
and the associated allocation is efficient.
Proposition 1 will be proved with the help of Table 2. Observe first that in column 1 of Table
2 the optimality conditions are listed with the implicit information y yU λ= . To avoid clutter
we slightly abuse the notation by writing
rr
y
λ λλ
= , kk
y
U UU
= and gg
y
μμ
λ=
&& etc.
The second column lists all marginal conditions in the benchmark market economy BM,
while y c yU pβ= is implicitly considered. Similar to our treatment of the first column, we
divide by c ypβ (or yU ) both sides of the equations contained in the lines 4 through 7 in the
second column. This operation has two effects: First, wU in these lines really represents the
6 It would also be important, in the first place, to secure the existence of such an equilibrium. We conjec-
ture that an equilibrium can be shown to exist but a rigorous existence proof is beyond the scope of the present study.
17
marginal rate of substitution ( )w yU / U for , , and c c c cw g k s v= . Moreover, cβ vanishes or,
equivalently, is set equal to one.
With these explanatory comments on Table 2 the proof of Proposition 1 is now straightfor-
ward. It suffices to replace in the second column of Table 2 all prices by the Lagrange multip-
liers or co-state variables that have been assigned to those prices in Proposition 1. Obviously,
this operation makes the second column of Table 2 coincide with the first column, line by
line. As a consequence, the market allocation is an equilibrium allocation and it is Pareto effi-
cient. This completes the proof of Proposition 1.
Proposition 1 provides two important pieces of information. First, it shows that our bench-
mark market economy is capable to support an efficient allocation and second, it demonstrates
how prices guide the allocation efficiently. All prices are positive (in case of an interior solu-
tion).
It is worth recalling how the equilibrium Lindahl’s prices are fixed. Conceptually the persona-
lized price must be set equal to the agent’s willingness-to-pay for the last unit of the public
good under consideration
r ggs s g
r
p Sp p S
S= = .
The far right side of this equation is the cultural-services firm’s cost savings from a marginal
substitution of the resource by cultural goods which leaves the output unchanged. This cost
savings exactly equals the firm’s willingness-to-pay for the last unit of cultural goods.
The equation
y ggc
y
p Up
U= ,
is straightforward, too. The price consumer-artist pays for her passive use of the stock of cul-
tural goods equals her marginal willingness-to-pay.
The RHS of the equation
y k r kkc
y r
p U p VpU V
= + ,
indicates that the consumer-artist’s (total) marginal willingness-to-pay for cultural capital is
the sum of her marginal willingness-to-pay as a consumer ( )y k yp U U and as a producer
( )r k rp V V .
18
In equilibrium, the consumer-artist’s personalized price for cultural services is given by
y s y ssc sK
y y
p U p Up p
U U= + > .
In other words, the price, the consumer-artist pays for consuming cultural services exceeds
her marginal willingness-to-pay for these services implying, under standard concavity condi-
tions, that she consumes more cultural services than she would do when following the
( )sc y s yp p U U= rule. The deviation from this rule is easily explained. After the consumer-
artist has purchased and consumed cultural services she resells them to firm K. The revenue
from this sale amounts to an effective reimbursement, in part, of her upfront expenditures for
cultural services. Hence sc sKp p− is the net price she really pays for her consumption of cul-
tural goods, and that net price is in fact equal to the marginal willingness-to-pay, s yU U .
A final remark relates to the assignments v gp μ= and sK kp μ= . In the optimal-control pro-
gram of the social planner, gμ and kμ are co-state variables, i. e. the shadow prices of the
stock of cultural goods ( )gμ and the stock of cultural capital ( )kμ in economic interpreta-
tion. In the benchmark market economy BM these stocks are not directly priced. But new
cultural goods serve as an investment into the stock of cultural goods. Hence v gp μ= means
that the stock of cultural goods is valued through the price of its investment good. The same
observation applies to the assignment sK kp μ= .
5 Missing markets and efficiency-restoring cultural tax-subsidy policy
In section 4 we showed that the optimal intertemporal allocation of the general model (GM)
can be “decentralized by prices” by means of market systems with competitive markets for all
commodities which include, in particular, Lindahl markets for cultural goods, cultural servic-
es and cultural capital. However, under the realistic assumption that information on prefe-
rences and technology is private, Lindahl markets cannot function smoothly unless one impli-
citly assumes that all agents reveal their characteristics (preferences and/or technologies)
truthfully. Therefore, the important question to ask is whether truthful revelation is in the de-
manders’ self-interest. Unfortunately the answer is no, since all agents have an incentive to
misrepresent their characteristics.
19
In a nutshell, Lindahl markets for public goods cannot be observed in reality. To move to-
wards a more realistic setting we therefore modify the market economy of section 4 by as-
suming that there are no Lindahl markets while all other competitive markets are still active
and function smoothly. More specifically, we will employ the assumption that the Lindahl
markets for the consumer-artists’ (passive) use of cultural goods and cultural capital are ab-
sent. These models will be marked by BL (Breakdown of Lindahl markets). Since the Lindahl
markets for the consumer-artists’ (passive) use of cultural goods and cultural capital do not
exist, in terms of the formal model, we set
= k kc gcp p p 0= ≡ . (34)
The model BL differs from the model BM only in the condition (34). Observe, that in BL
there are still Lindahl markets, namely the Lindahl market for cultural goods (as production
inputs) traded between firm G and the cultural-services firms and the Lindahl market for cul-
tural services traded between cultural-services firms and consumer-artists.7
Before we explore the allocative displacement caused by (34) in more detail and analyze the
options to restore efficiency by appropriate tax-subsidy schemes, it is useful to investigate the
impact of (34) on firm K. Consider firm K’s optimal-control problem
( )( )
K K
tk K sK sK Kk ,s
0
Max k p s e dtδτ τ∞
−⎡ ⎤− +⎣ ⎦∫ , subject to andK k Kk s k k kα= − ≤& , (35)
where and k sKτ τ are tax rates that are unconstrained in sign8. Suppose first, k sK 0τ τ= = . In
this case firm K doesn’t receive any revenue (subsidy) from selling its cultural capital. Since
firm K’s objective is to maximize the present value of its profits, any additional unit of cultur-
al capital “produced” implies negative profit. As a result, firm K’s best strategy is to cease
producing altogether. In terms of the formal model, firm K chooses Ks 0= , whenever
sKp 0> . But if sKp 0> , consumer-artists will choose cK cs s= , which is positive, in general.
Therefore the market for cultural services between firm K and consumer-artists is in excess
supply, and it follows that sKp 0= is a necessary equilibrium condition. With sKp 0= (and
k sK 0τ τ= = ) firm K has neither revenues nor costs and consumer-artists are indifferent in
their choice of any [ ],cK cs 0 s∈ . If k sK 0τ τ= = , it is therefore not restrictive to set cK cs s=
7 One may cast into doubt the realism of the remaining Lindahl markets. Yet we defend our procedure on
the grounds that in order not to blur the analysis by trying to deal with too many complex allocation prob-lems simultaneously, we have to reduce complexity.
8 kτ > 0 is a sales subsidy and sKτ < 0 [ sKτ > 0] is a subsidy [tax] on the purchase of cultural services.
20
and K c cs n s= such that firm K’s activity is completely reduced to the differential equation
K kk s kα= −& , as known from (5).
In principle, firm K could be revitalized by introducing non-zero tax rates. In fact, one could
simply set and k sK0 0τ τ> > to replace the missing market price and k sKp p , respectively.
We will refrain from pursuing this line of analysis in what follows, however, because such a
tax-subsidy scheme applied to firm K is an institutional design (of a public agency or public
enterprise) that doesn’t appear to be in the realm of relevance for practical cultural policy. In
other words, we assume in what follows that there is no market anymore for the exchange of
cultural services between consumer-artists and firm K implying that firm K is no player any-
more in our subsequent models. More precisely, the only “reminder” of firm K will be the
differential equation (5). The challenge will be to find tax-subsidy schemes, not relying on
(non-zero) and k sKτ τ , to correct for possible misallocations caused by the missing Lindahl
markets (cf. (34)).
But before we address this policy issue, some other points also need to be clarified. Up to now
we haven’t specified the response to the missing markets of all those agents who were former-
ly involved in transactions on those markets.
(a) Consider first the markets for cultural services traded between consumer-artists and
firm K. In the economy BM the consumer-artist spends the amount of money and sc c s cp s p s ,
respectively, on cultural services and receives the “reimbursement” sK cKp s . Since cK cs s= is
an equilibrium condition, the consumer-artist’s net expenditure on cultural services amounts
to ( )sc sK cp p s− in BM. As argued above, in case of (34) firm K doesn’t exist anymore in the
economy BL, implying sKp 0= (among other things). Yet it will turn out to be important for
our subsequent analysis to allow fees for cultural services to deviate from market prices.
Therefore we introduce a tax sτ and assume the consumer’s expenditures for cultural services
to be ( )sc sc cp sτ+ .
(b) In the absence of a Lindahl market for cultural capital traded between firm K and the con-
sumer-artists and with firm K’s disappearance, all consumer-artists enjoy the “prevailing level
of cultural capital” but they fail to understand and hence don’t take into account the process
of cultural-capital formation. In particular, they totally ignore the impact of their own contri-
butions through consumption of cultural services to the formation of cultural capital. Quite
obviously, the larger is the number of consumer-artists, the smaller is a consumer-artist’s con-
21
tribution to the formation of cultural capital and hence the more realistic it is for the consum-
er-artists to adopt the behavioral pattern of ignorance (cf. Pethig and Cheng, 2002).
(c) In the economy BM firm G sells cultural goods to two distinct groups of demanders: to
the cultural-services firms and to the consumer-artists. As outlined in (34) the market between
firm G and consumer-artists breaks down. In the absence of the Lindahl market for cultural
goods between firm G and consumer-artists, we assume again that consumer-artists are igno-
rant towards the dynamics of the stock of cultural goods, i.e. all consumer-artists take the pre-
vailing stock of cultural goods as given and enjoy its passive use for free.
Due to the absence of the Lindahl market for cultural goods traded between firm G and con-
sumer-artists, the market is reduced to firm G selling cultural goods to the cultural-services
firms only. To compensate firm G for the sales revenues foregone, c gc Gn p g , we will consider
a subsidy gτ for consumer-artists on the price at which they purchase cultural-goods stock
from firm G.
In their optimization calculus, ignorant consumer-artists take as given the “prevailing” stock
k, implying that and c cKk s are no longer in the set of their decision variables. The variable
cKs is dropped completely and ck is replaced by k. On the other hand, consumer-artists now
get for free their use of cultural capital and their passive use of the stock of cultural goods
which they had to pay for in the economy BM. Consequently firm K will not be paid anymore
for providing cultural capital to the consumer-artists. In fact, as argued above, firm K can now
be safely ignored.
Our subsequent analysis has two focal points: First we wish to demonstrate that in the absence
of corrective cultural policies the breakdown of markets causes allocative inefficiency and we
aim to characterize the misallocation, as far as possible. We call that situation the no-policy or
laissez-faire scenario. After that, the natural question is to ask whether and how efficiency
can be restored by suitable tax-subsidy schemes. The no-policy scenario is then the special
case where all these tax rates are set equal to zero.
5.1 The allocation in economy BL with and without corrective subsidy/taxes
The optimization program (28) of the cultural-services firms carries over from economy BM,
but the decision problems of firm G and consumer-artists need to be modified as follows:
● Firm G:
22
( )( )
G G
tg g G v Gg ,v
0
Max p g p v e dtδτ∞
−⎡ ⎤+ −⎣ ⎦∫ ,
subject to andG g Gg v g g gα= − ≤& , (36)
where g s gsp n p= . The associated Hamiltonian reads:
( ) ( ) ( )Gg g G v G g G g G GH p g p v v g g gτ ϕ α β⎡ ⎤= + − + − + −⎣ ⎦ , (37)
where gϕ is the co-state variable in economy BL. This specification of firm G’s decision
problem differs from that in section 4 in (30) only through the subsidy rate gτ on firm G’s
sales of cultural goods to the consumer-artists.
● Consumer-artist:
( )
( )v c c c
tc c cr , s , v , y
0
Max U g,k ,s ,v , y e dtδ∞
−∫ , subject to
( )c vv V r ,k= and ( )/v c r c c g c r v sc sc c y cp v p r g n p r p s p yπ τ τ+ + ≥ + + + + . (38)
Note that consumer-artist’s optimization calculus in (38) differs from that in (24) in some
components: The decision variables and c cg k in (24) are substituted by the state variables g
and k in (38), implying that the ignorant consumer-artist now takes as given the prevailing
stock of cultural goods and cultural capital, she receives the subsidy /g cg nτ on the price at
which she buys the cultural-goods stock (as passive-use). The associated Hamiltonian reads:
( ) ( )Cc c c vc v cH U g,k ,s ,v , y V r ,k vβ ⎡ ⎤= + −⎣ ⎦
( )c v c r c c g c r v sc sc c y cp v p r g / n p r p s p yβ π τ τ⎡ ⎤+ + + − − − + −⎣ ⎦ . (39)
For reference and comparison, the marginal conditions derived above are enumerated in the
third column of Table 2.
5.2 The efficiency-restoring cultural tax-subsidy policies
To explore how the market equilibrium fares in terms of allocative efficiency we compare the
marginal conditions of the efficient allocation with the marginal conditions derived in section
5.1 and report the results in
Proposition 2
23
(i) Set y yp λ= , r rp λ= , sc scp λ= , v gp μ= , s c scp n λ= , gc gcp λ= , gs gsp λ= ,
g s gs gp n λ τ= + , g c gcnτ λ= and sc kτ μ= − , where g k gc gs r sc y, , , , , andμ μ λ λ λ λ λ are
the values attained by the respective variables in the solution of (13) in section 3. Then
at each point in time there exists a general competitive equilibrium in economy BL
and the associated allocation is efficient.
(ii) If g sc 0τ τ= ≡ the general competitive equilibrium is inefficient.
Proposition 2 is verified by applying the same procedure as in the proof of Proposition 1.
Column 3 of Table 2 summarizes the first-order conditions characterizing the solutions of
(26), (28), (36) and (38). Similar to the treatment of column 1 and 2 in sections 3 and 4, we
divide by c ypβ (= yU ) both sides of the equations contained in the lines 4 through 7 in the
third column. With the assignment of prices and tax rates as shown in Proposition 2, column
3 of Table 2 is made to coincide with column 1. This match is straightforward for all rows
except for the rows 1 and 8.
Consider first the process of cultural-capital accumulation (row 8). To see that the subsidy
sc kτ μ= − renders the accumulation of cultural capital efficient, we carry out the following
thought experiment. Suppose, contrary to our setup, firm K is still active and with it the mar-
ket for cultural services between firm K and the consumer-artists. Let firm K solve (35) as-
suming sKp 0= (as argued above) but k c knτ λ= and sK kτ μ= . Hence the tax rates ( )k sK,τ τ
exactly replace the missing prices ( )k sKp , p . In this scenario the net price the consumer-artist
needs to pay for her consumption of cultural services is sc sK s kp p λ μ− = − (see above). In
economy BL where firm K is absent the consumer-artist’s net price for cultural services is
sc scp τ+ and due to Proposition 2 we have sc sc s kp τ λ μ+ = − . Hence the net price of cultural
services is the same in both cases. Next we consider the accumulation process of cultural-
goods stock (row 7). Now let firm G solve (36) assuming the subsidy rate g c gcn 0τ λ= > , the
subsidy hence replaces the missing price c gcn p , the consumer-artist needs to pay for her con-
sumption of cultural-goods stock is gc g cp / nτ= , such subsidy then renders the accumulation
of cultural-goods stock efficient. This observation implies that the efficient accumulation of
the cultural capital and the cultural-goods stock in economy BL is secured.
We now turn to the row 1 of Table 2 and observe that there is entry in column 1, 2 but no en-
try in column 3. The reason is, of course, the breakdown of the pertaining Lindahl markets in
24
the economy BL ( kc gcp p 0= ≡ ). In BL the intertemporal allocation of cultural capital and the
stock of cultural goods are not guided by demand-side signals anymore. Note, however, that
efficiency of the accumulation processes c c kk n s kα= −& and c c gg n v gα= −& is achieved as
long as the variables and c cs v take on their efficient values for all consumer-artists at each
point in time. This is secured by the assignment of those prices and subsidy rates that are
listed in Proposition 2.
The proof of Proposition 2 (ii) is simple. Modify the first sentence of Proposition 2 (i) by
setting g sc 0τ τ= ≡ , then consider the modified assignments of prices and subsidy rates in the
third column of Table 2, and finally juxtapose column 3, modified in this way, to column 1 of
Table 2 for comparing all rows pairwise. The entries in the rows 4 and 7 turn out not to match
anymore proving that the equilibrium allocation in economy BL is bound to deviate from the
Pareto-efficient allocation characterized by the marginal conditions of the first column of Ta-
ble 2. Hence the equilibrium allocation of economy BL is inefficient.
The central message of Proposition 2 is that the (equilibrium) allocation of the laissez-faire
economy is inefficient. The inefficiency of the laissez-faire economy, can be restored, how-
ever, by means of subsidizing (i) the consumer-artists’ creation of cultural goods at the rate
( )g c gcnτ λ= , and (ii) the consumer’s consumption of cultural services at the rate ( )sc kτ μ= − .
Though the empirical determination of the optimal levels of gτ and scτ is difficult, Proposi-
tion 2 still provides some conceptual basis for the design of an efficient cultural policy: this
policy should stimulate the consumer-artists’ creation of new cultural goods and consumption
of cultural services. The implementation of such efficient cultural policy can be, e.g. (i) the
active patronage of the government to the consumer-artists’ creation of cultural goods, and
thus the creational conditions become financially easier/more attractive, such that their crea-
tive activities can be encouraged; (ii) the governmental financial support on consumer-artists’
participation in cultural activities, therefore, the costs of the visits to museums and the atten-
dances of concert become less, such that the cultural activities can become more intensive.
The problem of underprovision of the cultural capital and the cultural-goods stock can be re-
medied through the efficient cultural policy that stimulates consumer-artists’ cultural activi-
ties.
6 Concluding remarks
25
This study provides a theoretical framework of cultural economics to help us to better under-
stand the real world. In our descriptive analysis, we first established a reference market model
in which the economy is endowed with a full set of perfectly competitive (Lindahl) markets
whose equilibrium is Pareto efficient. However, acknowledging that Lindahl markets don’t
emerge in the real world for reasons well understood by economists, we found that the lais-
sez-faire market allocation without Lindahl markets becomes inefficient. To correct such mi-
sallocation and internalize the positive externalities governmental intervention in the agents’
cultural activities is called for. We hence explored cultural policies in form of appropriate
subsidy/tax schemes that are capable to restore Pareto efficiency. In other words, the provi-
sion of cultural capital and cultural goods in the policy-supported market economy coincides
with their efficient provision in the benchmark model. The principal findings of our study are
summarized in the following three theses.
Thesis 1: In the laissez-faire market economy, consumers tend to ignore the beneficial exter-
nal effects of their cultural-services consumption on the other consumers through
accumulating cultural capital. The result is an underprovision of cultural capital.
Thesis 2: In the laissez-faire market economy, consumers tend to ignore the beneficial exter-
nal effects of their creations of cultural goods on the other consumers through aug-
menting the stock of cultural goods. The result is a suboptimally small stock of cul-
tural goods.
Thesis 3: Allocative efficiency can be restored by appropriate subsidies on the consumption
of cultural services and on the creation of cultural goods. These subsidies stimulate
the consumers’ demand for cultural services and the supply of cultural goods which
promotes the accumulation of both cultural capital and cultural goods.
Essentially, these theses were driven by our basic hypotheses that the consumption of cultural
services and the creations of cultural goods are not only beneficial for the individual consum-
ers but also contribute to form a “better” or a “more cultivated” society that is valued by all
members of society irrespective of their own cultural-services consumption and cultural-
goods creations. Therefore, the empirical relevance of our approach depends heavily on the
concepts of “cultural capital” and “cultural-goods stock”, and their measurability. Similarly,
as with the related notion of “social capital” or “human capital”, empirical measurement turns
out to be difficult. We are therefore left without straightforward evidence for the hypotheses
that members of society appreciate the accumulation of cultural capital and are proud of the
cultural goods created by themselves and their ancestors. Though the hypotheses may seem
trivial, they present demanding challenges for future research.
26
Acknowledgement
For helpful comments I am grateful to Ruediger Pethig.
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